# Engaging students: Box and whisker plots

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This submission comes from my former student Chris Brown. His topic: how to engage students when teaching box and whisker plots.

How could you as a teacher create an activity or project that involves your topic?

My all-time favorite TV show as a child was Pokémon. This show is still a staple amongst the young and even adult generation of today. The activity that I have created, was designed to take place after a formal lesson over how to create Box and Whisker plots. For this activity, students will be given a labeled bar graph of the Pokémon Type Distribution for generations 1 through 6 of Pokémon, which I have listed an online data source below. The students will be tasked with identifying the top 7 Pokémon types and creating a Box and Whiskers plots for each of those types. They will then go through and analyze the consistency of the creation of Pokémon for that specific type and then compare contrast this same box plot to any other box plot of their choice. The students will then make predications for the number of Pokémon for each of the top 7 Pokémon types, for generation 7 and base their reasoning in the box plots they created. Then the student will finally research the type distributions for the 7th generation of Pokémon, and discuss how the actual number compares to their prediction.

This is the online source for the type distributions for generations 1 – 6:

https://plot.ly/~powersurge360/6.embed

How does this topic extend what your students should have learned in previous courses?

From my experience, Box Plots are first taught in the early middle school years, in 6th or 7th grade. When constructing box plots by hand, in its essence, box plots require knowledge of how to order sets of numbers from least to greatest; an understanding and ability to find the maximum, minimum, median, and mean of a data set; and lastly, critical thinking and analytic skills developed from general course content. Box plots allow students to combine each of these skills to effectively analyze data sets with ease and compare different data sets with precision and accuracy. If any or all of these skills are not quite up to par, students will have an opportunity to develop them through box plots as they spend time creating them. For all students no matter their level, they will still gain better insight on how to properly analyze data and grow as analytical thinkers as they take the represented data and turn it into meaningful interpretations.

How can technology be used to effectively engage students with this topic?

In a classroom, I personally believe that Desmos is a wonderful online tool that can aid students in the understanding of how box and whisker plots function, and also a great place to check their work. Desmos, which is linked below, gives students the ability to list as many data points as they need to, and concurrently creates a box plot as they do so. In this way, students are able to see how singular data points can skew the data in significant and insignificant amounts. What I also love about Desmos is that, the list of data points does not have to be in any kind of order, so students do not have to worry about that tedious step! Desmos also lists the 5-point summary in two different places, on the box plot itself, and also on a drop-down menu, which is super convenient. Lastly, I love how Desmos also displays the mean of the data set as well, students can calculate the skew of the data, and definitively determine how it is skewed. This is a super visual, and interactive tool that will allow the student to manipulate box plots so seamlessly they will not be focused on the tediousness of the setup and solely on the concept.

The link to the Desmos setup is here: https://www.desmos.com/calculator/h9icuu58wn

# Engaging students: Box and whisker plots

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This submission comes from my former student Jesse Faltys. Her topic: how to engage students when teaching box and whisker plots.

A. ApplicationsHow could you as a teacher create an activity or project that involves your topic?

Students can take a roster of a professional basketball team and create a box and whiskers plot by using the players’ stats of height and weight.  As the teacher, you can provide these numbers to them. The weight should be left in pounds, but change the height measurement to inches.  The students could be placed in groups of 3 or 4 and given different team rosters.  First, have the student calculate the minimum, maximum, lower quartile, upper quartile, and median for their roster for both the weight and height. Then, have the students place the plots on large sheets of paper and present to the class.  As the students compare their plots, they can begin to see what effects the range of data has on the construction of each box and whisker plot. Depending on the knowledge of the students you might want them to all working on the same team.  As the teacher, you can remove one player’s stats from each group effectively changing the box and whiskers plots and having the students analyzing the data’s effect on the plot constructed from the same roster.

I actually used this in a lesson during my Step II class in a middle school classroom. I used information from the Illuminations website at http://illuminations.nctm.org/LessonDetail.aspx?ID=L737.

B. Curriculum – How can this topic be used in your students’ future courses in mathematics or science?

Any science course with a lab will require you to complete a formal lab write-up.  The data collected from your experiment will need to be represented in an organized manner.  The features of a box-and-whiskers plot will allow you to gather all your information and make observations off the data that your group and the class as a whole collected.  This information can be combined into one plot or the individual lab groups can be compared for any inconsistencies. A box-and-whisker plot can be useful for handling many data values. It shows only certain statistics rather than all the data. Five-number summary is another name for the visual representations of the box-and-whisker plot. The five-number summary consists of the median, the quartiles, and the smallest and greatest values in the distribution. Immediate visuals of a box-and-whisker plot are the center, the spread, and the overall range of distribution. This documentation will allow the student to make a formal analysis while putting together their formal lab write-up.

E. TechnologyHow can technology be used to effectively engage students with this topic?

1. Khan Academy provides a video titled “Reading Box-and-Whisker Plots” which shows an example of a collection of data on the age of trees. The instructor on the video goes through the representations of the different parts of the structure of the box and whiskers plot.  For our listening learners, this reiterates to the student what the plot is summarizing. http://www.khanacademy.org/math/probability/descriptive-statistics/Box-and-whisker%20plots/v/reading-box-and-whisker-plots

2. Math Warehouse allows you to enter the data you are using and it will calculate the plot for you.  After having the students work on their own plots, you can have them check their work for themselves.  This will allow for immediate confirmation if the student is creating the graph correctly with the data provided.  Also, this is allowing the visual learners to see what happens to the length of the box or whiskers when changes are made to the minimum, maximum or median. http://www.mathwarehouse.com/charts/box-and-whisker-plot-maker.php#boxwhiskergraph

3. The Brainingcamp is another website that allows for interaction between the different parts of the plot and the student.  This website allows for the students to see a group of data and the matching box-and-whiskers plot.  The student can then explore by manually changing different values and instantly seeing a change in the graph.  This involvement can stimulate questions to direct the student to complete understanding of the subject.  As a hands on learner, it allows the students to manipulate the plot immediately in different “what if” situations. http://www.brainingcamp.com/resources/math/box-plots/interactive.php

# Engaging students: Solving one-step and two-step inequalities

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This first student submission comes from my former student Jesse Faltys (who, by the way, was the instigator for me starting this blog in the first place). Her topic: how to engage students when teaching one-step and two-step inequalities.

A. Applications – How could you as a teacher create an activity or project that involves your topic?

1. Index Card Game: Make two sets of cards. The first should consist of different inequalities. The second should consist of the matching graph. Put your students in pairs and distribute both sets of cards.  The students will then practice solving their inequalities and determine which graph illustrates which inequality.
2. Inequality Friends: Distribute index cards with simple inequalities to a handful of your students (four or five different inequalities) and to the rest of the students pass of cards that only contain numbers. Have your students rotate around the room and determine if their numbers and inequalities are compatible or not. If they know that their number belongs with that inequality then the students should become “members” and form a group. Once all the students have formed their groups, they should present to the class how they solved their inequality and why all their numbers are “members” of that group.

Both applications allow for a quick assessment by the teacher.  Having the students initially work in pairs to explore the inequality and its matching graph allows for discover on their own.  While ending the class with a group activity allows the teacher to make individual assessments on each student.

B. Curriculum: How does this topic extend what your students should have learned in previous courses?

In a previous course, students learned to solve one- and two-step linear equations.  The process for solving one-step equality is similar to the process of solving a one-step inequality.  Properties of Inequalities are used to isolate the variable on one side of the inequality.  These properties are listed below.  The students should have knowledge of these from the previous course; therefore not overwhelmed with new rules.

Properties of Inequality

1. When you add or subtract the same number from each side of an inequality, the inequality remains true. (Same as previous knowledge with solving one-step equations)

2. When you multiply or divide each side of an inequality by a positive number, the inequality remains true. (Same as previous knowledge with solving one-step equations)

3. When you multiply or divide each side of an inequality by a negative number, the direction of the inequality symbol must be reversed for the inequality to remain true. (THIS IS DIFFERENT)

There is one obvious difference when working with inequalities and multiply/dividing by a negative number there is a change in the inequality symbol.  By pointing out to the student, that they are using what they already know with just one adjustment to the rules could help ease their mind on a new subject matter.

C. CultureHow has this topic appeared in pop culture?

Amusement Parks – If you have ever been to an amusement park, you are familiar with the height requirements on many of the rides.  The provide chart below shows the rides at Disney that require 35 inches or taller to be able to ride. What rides will you ride?

(Height of Student $\ge$  Height restriction)

 Blizzard Beach Summit Plummet 48″ Magic Kingdom Barnstormer at Goofy’s Wiseacres Farm 35″ Animal Kingdom Primeval Whirl 48″ Blizzard Beach Downhill Double Dipper 48″ DisneyQuest Mighty Ducks Pinball Slam 48″ Typhoon Lagoon Bay Slide 52″ Animal Kingdom Kali River Rapids 38″ DisneyQuest Buzz Lightyear’s AstroBlaster 51″ DisneyQuest Cyberspace Mountain 51″ Epcot Test Track 40″ Epcot Soarin’ 40″ Hollywood Studios Star Tours: The Adventures Continue 40″ Magic Kingdom Space Mountain 44″ Magic Kingdom Stitch’s Great Escape 40″ Typhoon Lagoon Humunga Kowabunga 48″ Animal Kingdom Expedition Everest 44″ Blizzard Beach Cross Country Creek 48″ Epcot Mission Space 44″ Hollywood Studios The Twilight Zone Tower of Terror 40″ Hollywood Studios Rock ‘n’ Roller Coaster Starring Aerosmith 48″ Magic Kingdom Splash Mountain 40″ Magic Kingdom Big Thunder Mountain Railroad 40″ Animal Kingdom Dinosaur 40″ Epcot Wonders of Life / Body Wars 40″ Blizzard Beach Summit Plummet 48″ Magic Kingdom Barnstormer at Goofy’s Wiseacres Farm 35″ Animal Kingdom Primeval Whirl 48″ Blizzard Beach Downhill Double Dipper 48″ DisneyQuest Mighty Ducks Pinball Slam 48″ Typhoon Lagoon Bay Slide 52″

Sports – Zdeno Chara is the tallest person who has ever played in the NHL. He is 206 cm tall and is allowed to use a stick that is longer than the NHL’s maximum allowable length. The official rulebook of the NHL state limits for the equipment players can use.  One of these rules states that no hockey stick can exceed160 cm.  (Hockey stick $\le$ 160 cm) The world’s largest hockey stick and puck are in Duncan, British Columbia. The stick is over 62 m in length and weighs almost 28,000 kg.  Is your equipment legal?

Weather – Every time the news is on our culture references inequalities by the range in the temperature throughout the day.  For example, the most extreme change in temperature in Canada took place in January 1962 in Pincher Creek, Alberta. A warm, dry wind, known as a chinook, raised the temperature from -19 °C to 22 °C in one hour. Represent the temperature during this hour using a double inequality. (-19 < the temperature < 22) What Inequality is today from the weather in 1962?